40 to 49 unbroken years
Names whose longest gap-free stretch of ranked years is between 40 and 49 years.
A year counts when any one of the seven registrars ranked the name that year, so a run can pass from one registrar to another. A break means no registrar ranked it that year — which usually means it fell below a published list's cut-off, never that no child received the name.
289 names, ordered by longest unbroken run first.